How to make a lightspeed scene
SOLUTION 1 POST PRO - Compositor/Directional blur

I started with a cube filled with static particles, all using an icosphere as the rendered object. Then I set up a Directional Blur node to animate the streak from the rendered image.



I also added some glare nodes to enhance the streaks as they get a bit transparent when distorted. I would render any spaceship interior on another layer so i could separate the zoom effect.

SOLUTION 2 POST PRO - Compositor/vector blur

You can use Vector Blur in the compositor.
I have made a larger volume of stars with an array of the initial cube. Then I fly the camera quite fast through it.
In the compositor I use a Vector node with a high number of samples (256).
In this way I can animate the streaks by moving the camera.



SOLUTION 3 POST PRO - In camera/Compositor



Use the moving camera again but this time turn on the actual motion blur feature in Cycles on the scene properties panel.
To emphasize the streak I have animated the size of the particle object (icosphere) as the camera speeds up.



I have added a second layer to render the cockpit image, which is parented to the camera location. 



I used the compositor to place the cockpit over the star image. I found that if the cockpit object was in the star layer, the particles would streak inside the cabin. Notice that the cockpit layer only has an object with an Emission material so i have turned the sample rate down to 1. This renders very fast.



SOLUTION 4 POST PRO - In camera/Particle hair



In this example I have used particle hair and animated the length via the Path end value. At the same time I am animating the position of the camera (with cockpit object).



Here you can see the array of planes with a hole in the middle for the camera to fly down.



In this frame is the rendered view and the display view showing the hair increasing in length.